Where will the books go?

Underground Robot Library, at the University of Chicago
Robot book fetcher at University of Utah
Book warehouse
University of Chicago Mansueto Library, profile
Inside the University of Chicago Mansueto Library

All the books will be moved to a warehouse where they can be scanned and made avalible in digital form to any local libraries.

Also any books requested by patrons from a local library can be transferred to that location, similar to what is now the inter-library loan service.

The University of Chicago introduced a robotic library system capable of holding 3.5 million books in one seventh the space of conventional libraries. The books are sorted by size and not by the Dewey decimal system. Engineers from Dematic, a firm that builds automated parts and storage-retrieval systems for Boeing, Ford and IBM, designed the five-story underground storage area which is managed by robotic cranes. Dematic has built 17 automated library systems worldwide similar to the one at the University of Chicago. As of 2013 the company has three more similar libraries under construction.

Resources:
Automated Storage and Retreaval Systems
U of U’s Automated Library System Proves Technology and Books Go Well Together
University of Chicago Robotic Library